Field of the Invention
The present invention generally relates to quantum gates and, more particularly, to controlled quantum gates.
Description of the Related Art
Entangled quantum states of light are in great demand in contemporary quantum technology. Photonic quantum information processing, and metrology are all based on exploiting special properties of non-classical multipath entangled states. Due to their high robustness against decoherence, and relatively simple manipulation techniques, photons are often exploited as the primary carriers of quantum information. A generally accepted encoding scheme using photons is dual rail encoding, in which logical qubit states |↑ and |↓ are encoded in two-mode Fock states |1, 0 and |0,1, respectively. In experimental photon implementations, these two modes are commonly associated with horizontal and vertical polarizations. An attractive feature of such an encoding is that single-qubit operations may be performed by the standard techniques of linear optics, using practically lossless beam splitters and phase shifters. However, when it comes to entangling photon-encoded qubits, a problem immediately arises: the absence of a photon-photon interaction for coupling the photons.
Optical Kerr nonlinearity can effectively couple photons through their interaction with a dispersive medium. However, due to the low photon numbers involved in typical quantum-information processing tasks, such nonlinearity is extremely weak and is of little practical use. Alternatively, an effective photon-photon interaction may be produced using ancilla modes and projective measurements. A quantum state generator can then be realized utilizing only linear-optical elements (beam splitters and phase shifters) in combination with photon counters, at the expense of the process becoming probabilistic. Knill, Laflamme, and Milburn (KLM) discovered that such a device is capable of transforming an initially separable state into entangled state. Since the transformation depends on the success of the measurement, the transformation has a probabilistic nature.
The paradigm of quantum computation is based on peculiar laws of quantum mechanics, which potentially allow manipulation and processing of information at exponentially faster rates as compared to classical computers. There exist at least two distinct schemes of implementing quantum computation. Historically the first scheme is based on the sequential application of a number of logical gates to elementary carriers of quantum information (qubits). A second scheme does not have a classical counterpart. Rather, it exploits the purely quantum phenomenon of wave function collapse under a measurement. A computation is performed by inducing non-unitary dynamics in a carefully prepared quantum state of multiple mutually entangled qubits by applying a sequence of measurements according to a desired computational algorithm. Such quantum states are called cluster states or, more generally, quantum graph states.
Since the cluster state paradigm offers better possibilities for error correction this scheme became the leading candidate for the physical realization of quantum information processing. From a physical point of view, photon based implementations of cluster states, where information is encoded in wave functions of single photons, has important advantages compared to other technologies.
Realizing a quantum computer is one of the most desirable goals in quantum information science, in which engineering photon entanglement is a key capability to implement the quantum system. According to contemporary research for qubits, entangling gates such as the C-phase gate or the CNOT together with single qubit operations are sufficient to create any kind of quantum network.
Cluster states generated by a Schioedtei assembly play a central role in a measurement-based one-way quantum computation approach. In this scheme, the entanglement resource is provided in advance through an initial, highly entangled multi-qubit cluster state and is consumed during the quantum computation by means of single-particle projective measurements. The feedforward nature of the one-way computation scheme renders the quantum computation deterministic, and removes much of the massive overhead that arises from the error encoding used in the standard quantum circuit computation model. FIG. 1 illustrates a scheme 10 for utilizing the output of a Schioedtei assembly to generate a four photon cluster state, |C4. This particular example employs the spots 1,2,3,4 and requires insertion of two half-wave plates 12, a SWAP gate 14 and a controlled-phase (C-Phase) gate 16. This scheme could be expanded to include the other eight spots to generate even larger cluster states.
A controlled phase (C-phase) gate has also been introduced, which uses a combination of first and second order interference to obtain C-phase operation in 1/9of the gates. Since the first-order interference requires stability of the setup on the order of less than the photon's wavelength, for multiphoton experiments more simple and stable implementations clearly are desirable.